Abstract: This is a competitive continuation of our Phase-I project. After successfully fulfilling all of its aims, a novel framework for optimal multi-surface and/or multi-object n-D biomedical image segmentation was developed, validated, and its practical utility demonstrated in clinical and translational image analysis tasks. This Phase-II proposal will develop several important extensions addressing identified limitations of the original framework while maintaining the ability of detecting optimal single and multiple interacting surfaces in n-D, including cylindrical shapes, closed-surface shapes, and shapes of complex topology. Novel methods will be developed for incorporation of shape-based a priori knowledge; substantial improvement of processing speed; and for interactive operator-guided segmentation. We hypothesize that by representing the segmentation problem in an arc-weighted graph (instead of the so-far utilized node-weighted graph), the 3-D and 4-D multi-surface multi-object optimal graph searching will offer significantly increased segmentation accuracy and robustness in volumetric image data from a variety of medical imaging sources, offering flexibility and higher processing speed, leading to real-time interactivity and practical applicability. We propose to: 1) Develop and validate a single- and multiple-surface n-D graph-based optimal segmentation method that uses arc-based graph representation, incorporates a priori shape knowledge using hard and soft constraints, and provides shape guidance while utilizing weighted combinations of edge-, region-, and shape-based costs. 2) Develop an approach for parallel (multi-core, multi-threaded) optimal graph search to significantly increase the processing speed and thus improving the method's applicability to higher-dimensional, multiply interacting, and overall larger problems. 3) Develop and evaluate an efficient real-time approach for interactive use of single- and multiple surface segmentations incorporating expert-user guidance while maintaining highly automated character of 3-D or 4-D segmentation. The developed methods will be evaluated against the Phase-I methods to demonstrate statistically significant performance improvements in a variety of tasks with data samples of sufficient sizes.